Method to limit stresses in cable tool drilling lines



March 10, 1953 Filed Oct. 3, 1949 J. F. KENDRICK 2,631,012

METHOD TO LIMIT STRESSES IN CABLE TOOL DRILLING LINES 2 SHEETSSHEET l INVENTOR John F. Kendrick Barf/ ATTORNEY Patented Mar. 10, .1953

OFFICE METHOD TO LIMIT STRESSES' IN CABLE- TOOL DRILLING LINES john F. Kendrick, Columbus; Ohio Application October 3, 1949, Serial No.- 119,236

6' Claims.

This is a continuation-in-part of Serial No. 694,182, Method and Apparatus to Limit Stresses in Elongated Elastic Structures, filed August 31, 1946, now abandoned, which was a continuationin-part of Serial No. 585,871, Method and Apparatus to Limit Stresses in Elongated Elastic Structures, filed March 31, 1945. Also pending is parent application Serial No. 112,858, filed August 29, 1949, Method for Limiting Stresses in Elongated Elastic Structures, which is a continuation of parent application Serial No. 585,871, filed March 31, 1945. Divisional applications Serial No. 115,282, filed September 12, 1949, Cable-Tool Drill With Electrical Variable Crank, and Serial No. 116,117, filed September 16, 1949, Cable-Tool Drill With Mechanical Variable Crank, which were currently pending", have been abandoned.

This inventionrelatesto the methods for the safe operation of elongated elastic structures, such as the cable tool. or churn drill, through a range of velocities, or strokes per minute, which necessitate passing back and forth through zones of vibrational resonance, which may develop destructive reactions.

A cable tool or churn drill consists of a bit, as part of a string of tools, attached to a drilling cable, which formerly was a manila rope but is now most often a wire line. Two forms of crank operated machines, the. walking beam. (Fig. 1) and spudder (Fig. 2), both of which are old in the art, are commonly used to reciprocate the drilling cable and tools, so that the impact of the bit against the formation will drill a hole or well bore. It will be observed that as the depth of the well increases, the length of the drilling cable is increased in proportion.

When the well is quite shallow, there is relatively little elasticity in the drilling cable and the mechanism conforms. approximately to the physical lawsof rigid bodies. A depth is reached eventually, depending on. the weight of the string of tools and the size, type, length and age of the drilling cable, where the elasticity. has increased to such a point, that the reaction of the bit must be analyzed by the laws of elasticity. The change from one system to the other is, of course, gradual and is generally complete at a depth of about 1,000 feet. Ultimately, generally around a depth of about 4,000feet', the system becomes so elastic that the method of operation must be changed to what amounts to tools, much like the way one form of'pile driver is operated. I This necessitates the use of a relatively loose hitch and a sufliciently long surface stroke to take the stretch out of. the drilling cable and raise the string of tools the required amount. I

, Either form of drill is, therefore, a m'odification of. a vibrating system with one degree of freedom, with forced vibrations and with viscous damping, the mathematics of which is fully developed in any one of a number of standard reference books, such as pages 1-113, particularly pages 38-51 of Vibration Problems in Engineering by Timoshenko, published by D. Van Nostrand C'o. Each departs slightly from a strict conformance to the theory clue to the impact of the bit'vv'ith the .forfiiatioh. My investigations have been directed towards the evaluations of the factors cdmsrismg such a system in terms of the conditions encountered in cable tool drilling. V

The general characteristic of the stroke of the tools is shown in Fig. 3. The vertical scale is the stroke of the toolsjexpressed as multiples of the surface stroke} The elastic drilling cable has a natural or fundamental frequency, and the operation of the" walking beam or spudder arm is a forced vibration with a" fixed frequency at any given number" of strokes per minute; The horizontal scale is the ratio of the period of the natural frequency of the drilling cable to the period of the vibration of the' walking beam or spudder arm, andthis scale can be expressedin strokes per minute for any fixed set of condi-' tions,. by methods well known to those familiar with vibrational mechanic's. Whenever there are two or more vibrations working together, we encounter a critical velocity or resonance at which the frequencies are equal or nearly equal, whichi's calledthe'peak of" vibrational resonance in this specification, Where the amplitude or half-strokeof'the' resultant vibration is magnifled greatly. Adjacent such peaks are zones of destructive vibrationalreactions. It'will be observed in Fig. 3, therefore, that at relatively low strokes pe'r' minute off the drilling mechanism, the stroke of the bit" is equal to the surface stroke; at the critical" velocity of the resonance point, thestroke' of the bit is magnified greatly,

andat high speeds the stroke of the bit be drilling that the zone of vibrational resonance" generally produces destructive reactions in the string of tools suificiently severe to mushroom the bit, increase the frequency of pin failure and to throw slack into the drilling cable. It is not a practical zone, therefore, in which to operate the drilling mechanism. As a result, it has become customary, to limit the strokes per minute, when drilling, to those corresponding to approximately 0.5 to 0.6 on the horizontal ratio scale of Fig. 3. As the zone of vibrational resonance occurs at a lower number of strokes per minute as the depth of the well increases, it is necessary to operate the drilling mechanism at a fewer number of strokes per minute. In one field in West Virginia, it is customary to operate at 45 S. P. M. at a depth of about 500 feet and this is progressively reduced to about 25 S. P. M. at a depth of 3,000 feet. As the drilling speed is a function of the impacts per minute, this represents a serious loss in drilling efiiciency. An improvement of from 200 to 300 per cent, in drilling efficiency should result from making it possible to operate the drilling mechanism above the zone of vibrational resonance.

In order to operate the drilling mechanism above the zone of vibration resonance, it will be necessary to protect the various parts of the mechanism when passing back and forth through the zone. The preferred method and apparatus for affording the required protection is disclosed in my co-pending application, Serial No. 112,858, filed August 29, 1949, which is a continuation of Serial No. 585,871, filed March 31, 1945, wherein precision control of the drilling mechanism is effected by reducing or eliminating the throw of the crank, while passing through the zone of vibrational resonance, and then adjusting the throw of the crank as required for drilling, while the machine is in operation.

An alternate method consists of increasing the strokes per minute, or motion as it is called. by drillers, rapidly so as to pass through the resonance stage fast enough to prevent the stroke of the bit from becoming excessive. However, it is impossible to guard against the bit being cperated for a few strokes with an impact sufiicient- 1y large to seriously injure its cutting edge. Also, the weight of the drilling cable is such, on the deeper wells, that the cable may be damaged before the drilling motion settles down.

Some degree of safety can be secured by setting the tools on bottom and operating on the stretch of the drilling cable, while passing through the zone of vibrational resonance, and then ad-' justing them for drilling by raising them off bottom, as required. This can be done with the usual spudder movement, without any change in the apparatus. With the walking beam, it is necessary to replace the common mechanically operated temper screw with a hydraulically operated feed cylinder, as is described in detail elsewhere in this specification.

It is an object of this invention to provide a new and economically important method of operating elongated elastic structures, such as the cable tool drill. It is another object of this invention to make it safe to operate elongated elastic structures, such as the cable tool drill, over a materiallly wider range of strokes per minute, under a given set of conditions, thereby increasing the operating efficiency of such structures.

It is a further object of this invention to teach the method of avoiding the hazards of operating such structures in the zone of vibrational resonance and safely securing the advantages of op- 4 crating such structures above the zone of vibra tional resonance.

Another object of this invention is to teach the method of setting the tools of a cable tool drill on bottom, while the strokes per minute are below the zone of vibrational resonance, working on the stretch of the drilling cable, while the strokes per minute are increased to a point above the zone of vibrational resonance, then raising the tools as required for drilling.

Further objects of the invention will appear from the following description, in which I have set forth the preferred embodiment of my invention.

For a further understanding of the nature of the invention and the detailed features of construction thereof, as well as additional objects and advantages, reference is to be had to the accompanying drawings, wherein:

Fig. l is a diagrammatic side elevational view of a standard or walking beam type of cable tool drill, with a hydraulic feeding mechanism positioned on top of the walking beam;

Fig. 2 is a diagrammatic side elevational view of the spudder type of cable tool drill;

Fig. 3 is a graph diagram showing the theoretical length of the stroke of the suspended weight in a vibrating system with one degree of freedom;

Fig. 3a is a graph diagram showing how the resonance peak occurs at a lower number of S. P. M. as the depth of the well increases;

4 is a diagrammatic top plan View of the walking beam, with the hydraulic feeding device mounted thereon.

Referring to Fig. 1, showing the principal parts of the walking beam type of cable tool drill, the numeral l is the band wheel driven by belt 2 from a motor or engine (not shown). A crank 3 is mounted on the band Wheel shaft and carries a wrist pin 3. The wrist pin is connected to a pitman 5, which, at its upper end, is connected to one end of a walking beam 6, the latter being supported for oscillation by the usual Samson post. On top of the walking beam, at the crank end thereof, is positioned a hydraulic feeding cylinder 7, which is connected to a clamp 8, which grips a drilling cable 9, by means of a piston rod 2, a cross yoke 13, and a pair of flexible cables or chains i l and Ma. guided b sheaves l5 and 55a (Fig. 4). The bit and other parts of the string of tools (not shown) are suspended from the lower end of the drilling cable. In operation, the crank imparts an oscillating motion to the beam, which in turn reciprocates the drilling cable. Thus, the bit is able to strike the formation with impact, which effects the drilling.

The hydraulic feeding mechanism is shown in greater detail in Fig. 4, in which it is a cylinder in which is positioned a piston ii and a piston rod !2, working back and forth through stuiiing box I9. A crosshead yoke i3, slidingly guided by the walking beam is attached to the outer end of the piston rod I2, and flexible cables or chains M and [4a are attached to crosshead yoke l3 and are guided by sheaves i5 and it'd, while shields 23 and 23a prevent the cables or chains from being snapped out of the sheave grooves by the whip of the drilling cable 9. Hydraulic power is supplied by the usual positive pressure pump (not shown) to conduits 2i! and 280:, through control valve 2-! to conduits 22 and 22a, which are connected to the outer ends of cylinder 15. The piston H can, therefore, be moved in either direction or held stationary, at the will of an operanemia ator, the details of the control being familiar to those versed in the art. Rope clamp 8, being attached to the ends of flexible cables or chains 14 and Ma, is raised or lowered or held stationary in synchronism with piston H, at the will of the operator, thereby making the quick and precise adjustment of the drilling hitch possible.

In Fig. 2, which shows the principal parts of the spudder type of cable tool drill, Ill is an engine, which drives the crank 3a through a belt 2a and wheel la, mounted on a shaft common to the crank 3a. The crank drives the wrist pin 4a, which causes the upper end of the pitman 5a to oscillate the spudder arm II, which imparts a reciprocating motion to the drilling cable 9a. This causes the bit (not shown) suspended from the lower end of the drilling cable to strike the formation with impact, which effects the drilling. As is well known by this skilled in the art, the bit (not shown) can be raised or lowered by winding and unwinding the drillingcable 90:, on or from the bull wheel 24 while the spudder arm H is operating, and the quick and precise adjustment of the hitch is, therefore, possible.

In operation, a drilling cable usually attains such length as to acquire sufficient elasticity to conform closely to the principal characteristics of a vibrating system, having one degree of freedom with 'forced vibrations and viscous damping. The Sucker-Rod Pump as a Problem in Elasticity by John F. Kendrick and Paul D. Cornelius, published on pages 15 to 31 inclusive, of volume 123, Transactions of the American Institute of Mining and Metallurgical Engineers, 1937, conveniently brings together the principal formulas for such a system. Fig. 31s the graphical solution of Formula 1, page 1'7, preceded by plus and minus, with l substituted for (Z2 to give a dimensionless factor, thus:

ds=half thesubsurfacestroke, i-ns., T =period of natural-vibration,sec., T1=period of forced vibration of reciprocating mechanism, sec, :SG/S. P. M.,

and v u =damping factor.

The upper half of this "group of curves only'is most generally reproduced, and it is theamp'litude or half stroke of the sub-surface vibration. Prefixing plus and minus results in the mirror image of the upper group of curves, so that an upper with its corresponding lower curve gives the boundary of the displacement or the full length of the resultant sub-surface vibration or stroke in multiples of the surface stroke, as given on the vertical scale. The different curves, marked-0.3, 0.5 etc-are the boundary of the resultant'strokeunder different friction factors.

A drilling cableis an elastic body, which, when excited, as by the reciprocating motion at the surface, will vibratewith a natural vibration which has a definite period in seconds per cycle, which is the reciprocal of the frequency in cycles per second. lhe period T in'seconds, per cycle of the natural vibration, is equal to 0.3195 times the square root of the static deflection, which will be explained later. The period of the forced vibration or the surface reciprocation, Tr inseconds' per cycle, is, naturally, equal to 60 divided by the S. P. M. The horizontal scale of Fig. his the ratio R of the natural vibration T divided by the period of the forced vibration T1. The horizontal scale maybe converted to S. P. M. N by multiplying R by 60 and dividing by the period of the natural vibration T, as given by Formula 2, page 20', of Kendrick et al., thus-z Where N =strokes per minute of the reciprocating mech- 'anism R=rati0 T/T1=0.2f, 0L3,etc,,.

and

T=period of the natural vibration, sec.

where e=elongation, in.,

P=force producing stretch, 1b., L=length of'spring, ind, A=area, sq. -'in.,

and

E =modulus of elasticity.

In the case of .the cable tool drill, the aging of the drilling cable is evidenced by an increase in the magnitude of Youngs Mcdu'lus'E. The location of the peak of vibrational resonanceshould therefore be computed for a maximum and minimum modulus, using the manufacturers value for the minimum modulus and the average of this and thirty million, the modulus for steel, as the maximum modulus. This results in two loci of thepeak, as-shown in Figpsa. Fig. 3a is plotted by computing the periods of the-natural vibration of the system, using'theminimum and maximum moduli, and the physical data for the conditions being analyzed, as indicated at the right edge for different'depthsyanddividing 60 by the periods'T, toget S. P. M., at vibrational resonance or when R'is equalto '1.

:In the operation of the --drill,"the point of 'operation would be determined as above. Actual drilling involves the additional problems of controlling the impact and therateof feed of the bit. A solution to these problems is disclosed in my co-pendin-g application Serial N0.590,498, filed April 26, 1945, Drilling Motion Indicator for Cable-Tool Drill. This application issued January 29, 1952, as the following'patents:2,584,026, Apparatus for Drilling Motion Indicators; No.

2,584,027, Drilling Cable Withlnsulated- Conductor; No. 2,584,028, Impact Switch. Operation below the resonance peak 'is-at a frequency or S. P. M. which are less than whenoperating above the peak,'and with-anamplitude of-vibra tion or reciprocation or length ofstroke which. is greater than when operating above.

As stated, it is customary-todrill, atthepresent. time, with :a speedor "motioir strokes perminute corresponding approximately "to 0.5- on the horizontal ratio scale. The problem is to protect thecomponents of the drilling mechanism, while the speed or motion in strokes per minute is increased to a point approximating say 1.75 on the'h-orizontal ratio scale, from the destructive reactions set up in the zone of vibrational resonance, extending from approximately 0.5 to approximately 1.5 on the horizontal ratio scale.

It is, of course, impossible for the bit to move farther than the bottom of the hole, and the difference between a tight and loose hitch is a question of the velocity of the bit at theinstant of impact with the bottom of the hole. Referring to Fig. 3, the lower curves mark the path of the bit, when it is hanging free, as the strokes per minute are increased. If we assume that we are drilling at 0.5 on the horizontal ratio scale of Fig. 3, the hitch is adjusted so that the bit will strike the formation of a few inches above the lower curve and the balance of the stroke is completed on the contraction and stretch of the drilling cable. In a loose hitch, therefore, the adjustment is made so that the bit will strike the formation at a point considerably higher in relation to the lower curve, and much more of the stroke is completed on the contraction and stretch of the drilling cable. The velocity of the bit is, therefore, higher, at impact, for a loose hitch than it is for a tight hitch. Once a drilling hitch has been effected below the zone of vibrational resonance, the practical efiect of inc-reasing the strokes per minute is to increase the velocity of the bit at the point of impact, and as the magnitude of the impact is proportional to the square of the velocity at the instant of impact, a point is soon reached where the impact is so great that the cutting edge of the bit is uselessly battered and the frequency of mechanical failure is greatly increased. However, Fig. 3 shows that above the zone of vibrational resonance, the stroke of the bit becomes shorter automatically, and, with the judicious choice of the length of the surface stroke, the impact can be limited to what the string of tools operate with a reasonable frequency of mechanical failure, and the drilling speed will be increased due to the increased impacts per minute.

The string of tools can be protected, as the strokes per miniit'e are increased through the zone of vibrational resonance, by setting the bit onthe bottom of the hole, and operating mainly on the stretch of the drilling cable, until the desired strokes perminute have been reached. The string of tools is then raised oii bottom, and the desired drilling hitch is manipulated.

As thestring of tools is run into the hole, the dead weight of the cable and tools act on the helical structure of the cable to cause it to untwist and materially increase its length. The reciprocation of the drilling cable causes the swiveling element of the rope socket to function, permitting the cable to retwist and again shorten its length. It will be preferable, therefore, to make a hitch below the peak of resonance, then set the tools onbottom, sufiiciently to eliminate the reciprocation of the string of tools, increase the frequency of the reciprocation or the strokes per minute of the upper end of the cable to a point above the zones of destructive reactions adjacent the resonance peak and then reel in the cable to raise the string of tools until the bit is reciprocating and then make the usual adjustments until the drilling is satisfactory. On stopping, the cable will be run intothe hole until the 8 string of tools no longer reciprocates, whereupon the clutch is disengaged or the engine stopped.

An alternate method will be to eliminate the making of the hitch below the peak of resonance. The string of tools will be run int-o the hole and set on bottom, the cable being slacked enough so that the tools will not reciprocate, when the clutch is engaged. Then the frequency or strokes per minute of the upper end of the drilling cable are increased to a point above the zones of destructive reactions adjacent the resonance peak. Then the cable is reeled in, raising the tools off bottom until the bit is reciprocating, and the adjustments made for satisfactory drilling. In the deeper drilling, the shortening of the cable, due to retwisting, may pull the bit to such a height that it will make a number of strokes without striking the bottom of the hole. This will needlessly increase the peak stress in the drilling cable and this alternate method is not to be recommended for this reason. Stopping will be efiected as in the first method. Where the ordinary stretch of the drilling cable is insuflicient, the stroke of the drilling jar, regularly incorporated in the string of tools, may be utilized, and it will always be advisable to traverse the zones of destructive reactions, adjacent the peak of resonance, as rapidly as possible.

This invention, therefore, teaches a practical method or" limiting the stresses while passing back and forth through the zones of destructive reactions adjacent the peak of resonance. Therefore, the industry will be able to benefit from the reduced drillin costs, resulting from the increased drilling speed clue to the greater number of impacts per minute possible by operating above the resonance peak.

What I claim as new and desire to secure by Letters Patent is:

l. The method of limiting the stresses in the elements of an elongated elastic metallic structure, vertically disposed in a hole, with a weight at its lower end, arranged to be lowered into and raised out of a hole with a closure at its lower end and to be reciprocated at its upper end at variable frequencies, to traverse zones of destructive vibrational reactions adjacent to peaks of vibrational resonance, comprising the steps of lowering the structure into the hole, until the weight is supported by the closure, so as to eliminate the reciprocation of the weight, reciprocating the upper end of the structure at a frequency below the peak, increasing the frequency of the reciprocation of the upper end of the structure to a point above the peak and then raising the structure so that the weight can reciprocate.

2. The method of limiting the stresses in the elements of an elongated elastic metallic structure, vertically disposed in a hole, with a weight at its lower end, arranged to be lowered into and raised out of a hole with a closure at its lower end and to be reciprocated at its upper end at variable frequencies, to traverse zones of destructive vibrational reactions adjacent to peaks of vibrational resonance, comprising the steps of lowering the structure into the hole until the weight is supported by the closure, so as to eliminate the reciprocation of the weight, while operating at a frequency of reciprocation oi the upper end above the peak and then reducing the frequency of the reciprocation of the upper end of the structure to a point below the peak.

3. The method of limiting the stresses in the elements of an elongated elastic metallic structure, vertically disposed in a hole, with a weight at its lower end, arranged to be lowered into and raised out of a hole with a closure at its lower end and to be reciprocated at its upper end at variable frequencies, to traverse zones of destructive vibrational reactions adjacent to peaks of vibrational resonance, comprising the steps of reciprocating the upper end of the structure at a; frequency below the peak, lowering the structure into the hole, until the weight is supported by the closure, so as to eliminate the reciprocation of the weight, increasing the frequency of the reciprocation of the upper end of the structure to a point above the peak and then raising the structure, so that the Weight can reciprocate.

4. The method of limiting the stresses in the elements of a cable-tool drill, including an elastic drilling cable, with a bit, as part of a string of tools, at its lower end, arranged to be lowered into and raised out of a hole with a closure at its lower end and to be reciproca-ted at its upper end at variable frequencies, to traverse zones of destructive vibrational reactions adjacent to peaks of vibrational resonance, comprising the steps of lowering the drilling cable into the hole, until the bit is supported by the closure, so as to eliminate the reciprocation of the bit, reciprocating the upper end of the cable at a frequency below the peak, increasing the frequency of the reciprocation of the upper end of the cable to a point above the peak and then raising the cable, so that the bit can reciprocate.

5. The method of limiting the stresses in the elements of a cable-tool drill, including an elastic drilling cable, with a bit, as part of a string of tools, at its lower end, arranged to be lowered into and raised out of a hole with a closure at its lower end and to be reciprocated at its upper end at variable frequencies, to traverse zones of destructive vibrational reactions adjacent to peaks of vibrational resonance, comprising the steps of lowering the drilling cable into the hole until the bit is supported by the closure, so as to eliminate the reciprocation of the bit, while operating at a frequency of reciprocation of the upper end above the peak and then reducing the frequency of the reciprocation of the upper end of the cable to a point below the peak.

6. The method of limiting the stresses in the elements of a cable-tool drill, including an elastic drilling cable, with a bit, as part of a string of tools, at its lower end, arranged to be lowered into and raised out of a hole with a closure at its lower end and to be reciprocated at its upper end at variable frequencies, to traverse zones of destructive vibrational reactions adjacent to peaks of vibrational resonance, comprising the steps of reciprocating the upper end of the cable at a frequency below the peak, lowering the cable into the hole, until the bit is supported by the closure, so as to eliminate the reciprocation of the bit, increasing the frequency of the reciprocation of the upper end of the cable to a point above the peak and then raising the cable, so that the bit can reciprocate.

JOHN F. KEN'DRICK.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 506,204 Button Oct. 10, 1893 854,606 Rourke May 21, 1907 1,049,481 Herman et al Jan. 7, 1913 1,165,723 Shoup Dec. 28, 1915 1,354,769 Leonard Oct. 5, 1920 1,511,990 Hartzell Oct. 14, 1924 1,655,062 Kammerer et a1 Jan. 3, 1928 1,707,568 Ramsey Apr. 2, 1929 1,951,536 Swift Mar. 20, 1934 2,126,992 Hall Aug. 16, 1938 2,319,485 Ala-brune May 18, 1943 FOREIGN PATENTS Number Country Date 300,850 Germany 1916 308,325 Germany Mar. 27, 1917 OTHER REFERENCES Timoshenk-o-Vibration Problems in Engineering, 2nd. Ed. 1937, pp. 38-49.

Carstarphen-The CSM Magazine, pp. 15-30, Sept. 1931.

Kendrick et al.Tras. A-SME, vol. 123, pp. 15-31, 1937.

Sprengling et al.Drilling Practice, pp. 64-72, 1940.

Kendrick-Oil and Gas Journal, Oct. 7, 1948, Towards a Better Understanding of Cable Tool Drilling.

Slonneger-Production Practice, pp. 179-188, 1937.

Peterson-Petroleum Engineer, pp. 33-36, Feb. 1939.

Kendrick-Oil and Gas Journal, Dec. 13, 1947, Drilling Stresses Present in Cable-Tool Operations, Part I.

Kendrick0il and Gas Journal, July 1, 1948, Drilling Stresses Present in Cable-T001 Operations, Part II.

Kendrick-Oil and Gas Journal, May 26. 1949, Use of Cable Tools in Wet Holes and at High Stroke Rates.

Uren-Petroleum Production Engineering, vol. 1,1 11. -172, 2nd Ed., 1934. I 

